Generation of three-qubit entangled states using superconducting phase qubits


Entanglement is one of the key resources required for quantum computation1, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers2. In superconducting devices3, two-qubit entangled states have been demonstrated and used to show violations of Bell’s inequality4 and to implement simple quantum algorithms5. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways6. These are typified by the states |GHZ〉 = (|000〉 + |111〉)/ and |W〉 = (|001〉 + |010〉 + |100〉)/. Here we demonstrate the operation of three coupled superconducting phase qubits7 and use them to create and measure |GHZ〉 and |W〉 states. The states are fully characterized using quantum state tomography8 and are shown to satisfy entanglement witnesses9, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.

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Figure 1: Protocols for generating entangled states.
Figure 2: Device description and operation.
Figure 3: Generation of entangled states in the time domain.
Figure 4: Quantum state tomography of |GHZ〉 and |W〉.


  1. 1

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

    Google Scholar 

  2. 2

    Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010)

    CAS  Google Scholar 

  3. 3

    Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008)

    CAS  Google Scholar 

  4. 4

    Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009)

    CAS  Google Scholar 

  5. 5

    DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

    CAS  Google Scholar 

  6. 6

    Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Google Scholar 

  7. 7

    McDermott, R. et al. Simultaneous state measurement of coupled Josephson phase qubits. Science 307, 1299–1302 (2005)

    CAS  Google Scholar 

  8. 8

    Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006)

    CAS  Google Scholar 

  9. 9

    Acín, A., Bruss, D., Lewenstein, M. & Sanpera, A. Classification of mixed three-qubit states. Phys. Rev. Lett. 87, 040401 (2001)

    Google Scholar 

  10. 10

    Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    CAS  Google Scholar 

  11. 11

    Shi, Y. Both Toffoli and controlled-NOT need little help to do universal quantum computation. Quantum Inf. Comput. 3, 84–92 (2003)

    Google Scholar 

  12. 12

    Lanyon, B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys. 5, 134–140 (2008)

    Google Scholar 

  13. 13

    Monz, T. et al. Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102, 040501 (2009)

    CAS  Google Scholar 

  14. 14

    Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)

    CAS  Google Scholar 

  15. 15

    Galiautdinov, A. & Martinis, J. M. Maximally entangling tripartite protocols for Josephson phase qubits. Phys. Rev. A 78, 010305 (2008)

    Google Scholar 

  16. 16

    DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature doi:10.1038/nature09416 (this issue).

  17. 17

    Wei, L. F., Liu, Y. X. & Nori, F. Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits. Phys. Rev. Lett. 96, 246803 (2006)

    CAS  Google Scholar 

  18. 18

    Matsuo, S. et al. Generation of macroscopic entangled states in coupled superconducting phase qubits. J. Phys. Soc. Jpn 76, 054802 (2007)

    Google Scholar 

  19. 19

    Schuch, N. & Siewert, J. Natural two-qubit gate for quantum computation using the XY interaction. Phys. Rev. A 67, 032301 (2003)

    Google Scholar 

  20. 20

    Lucero, E. et al. High-fidelity gates in a single Josephson qubit. Phys. Rev. Lett. 100, 247001 (2008)

    Google Scholar 

  21. 21

    Neeley, M. et al. Emulation of a quantum spin with a superconducting phase qudit. Science 325, 722–725 (2009)

    CAS  Google Scholar 

  22. 22

    Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009)

    CAS  Google Scholar 

  23. 23

    Mermin, N. D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838–1840 (1990)

    CAS  Google Scholar 

  24. 24

    Pan, J.-W., Bouwmeester, D., Daniell, M., Weinfurter, H. & Zeilinger, A. Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement. Nature 403, 515–519 (2000)

    CAS  Google Scholar 

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Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. This work was supported by IARPA under grant W911NF-04-1-0204. M.M. acknowledges support from an Elings Fellowship.

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M.N. fabricated the sample, performed the experiments and analysed the data. J.M.M. and E.L. designed the custom electronics. H.W. and T.Y. contributed to software infrastructure. All authors contributed to the fabrication process, qubit design, experimental set-up and manuscript preparation.

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Correspondence to John M. Martinis.

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The authors declare no competing financial interests.

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Supplementary Information

This file contains Supplementary Methods and Discussion describing experimental methods and analysis procedures, Supplementary Tables 1-2, Supplementary Figure 1 with legend and additional references. (PDF 276 kb)

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Neeley, M., Bialczak, R., Lenander, M. et al. Generation of three-qubit entangled states using superconducting phase qubits. Nature 467, 570–573 (2010).

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